A mutable reduction operation that
accumulates input elements into a mutable result container, optionally transforming
the accumulated result into a final representation after all input elements
have been processed.

Here we use widgets, a Collection<Widget>,
as a source for a stream, and then perform a filter-map-reduce on the stream
to obtain the sum of the weights of the red widgets. (Summation is an
example of a reduction
operation.)

The key abstraction introduced in this package is stream. The
classes Stream, IntStream,
LongStream, and DoubleStream
are streams over objects and the primitive int, long and
double types. Streams differ from collections in several ways:

No storage. A stream is not a data structure that stores elements;
instead, it conveys elements from a source such as a data structure,
an array, a generator function, or an I/O channel, through a pipeline of
computational operations.

Functional in nature. An operation on a stream produces a result,
but does not modify its source. For example, filtering a Stream
obtained from a collection produces a new Stream without the
filtered elements, rather than removing elements from the source
collection.

Laziness-seeking. Many stream operations, such as filtering, mapping,
or duplicate removal, can be implemented lazily, exposing opportunities
for optimization. For example, "find the first String with
three consecutive vowels" need not examine all the input strings.
Stream operations are divided into intermediate (Stream-producing)
operations and terminal (value- or side-effect-producing) operations.
Intermediate operations are always lazy.

Possibly unbounded. While collections have a finite size, streams
need not. Short-circuiting operations such as limit(n) or
findFirst() can allow computations on infinite streams to
complete in finite time.

Consumable. The elements of a stream are only visited once during
the life of a stream. Like an Iterator, a new stream
must be generated to revisit the same elements of the source.

Stream operations are divided into intermediate and
terminal operations, and are combined to form stream
pipelines. A stream pipeline consists of a source (such as a
Collection, an array, a generator function, or an I/O channel);
followed by zero or more intermediate operations such as
Stream.filter or Stream.map; and a terminal operation such
as Stream.forEach or Stream.reduce.

Intermediate operations return a new stream. They are always
lazy; executing an intermediate operation such as
filter() does not actually perform any filtering, but instead
creates a new stream that, when traversed, contains the elements of
the initial stream that match the given predicate. Traversal
of the pipeline source does not begin until the terminal operation of the
pipeline is executed.

Terminal operations, such as Stream.forEach or
IntStream.sum, may traverse the stream to produce a result or a
side-effect. After the terminal operation is performed, the stream pipeline
is considered consumed, and can no longer be used; if you need to traverse
the same data source again, you must return to the data source to get a new
stream. In almost all cases, terminal operations are eager,
completing their traversal of the data source and processing of the pipeline
before returning. Only the terminal operations iterator() and
spliterator() are not; these are provided as an "escape hatch" to enable
arbitrary client-controlled pipeline traversals in the event that the
existing operations are not sufficient to the task.

Processing streams lazily allows for significant efficiencies; in a
pipeline such as the filter-map-sum example above, filtering, mapping, and
summing can be fused into a single pass on the data, with minimal
intermediate state. Laziness also allows avoiding examining all the data
when it is not necessary; for operations such as "find the first string
longer than 1000 characters", it is only necessary to examine just enough
strings to find one that has the desired characteristics without examining
all of the strings available from the source. (This behavior becomes even
more important when the input stream is infinite and not merely large.)

Intermediate operations are further divided into stateless
and stateful operations. Stateless operations, such as filter
and map, retain no state from previously seen element when processing
a new element -- each element can be processed
independently of operations on other elements. Stateful operations, such as
distinct and sorted, may incorporate state from previously
seen elements when processing new elements.

Stateful operations may need to process the entire input
before producing a result. For example, one cannot produce any results from
sorting a stream until one has seen all elements of the stream. As a result,
under parallel computation, some pipelines containing stateful intermediate
operations may require multiple passes on the data or may need to buffer
significant data. Pipelines containing exclusively stateless intermediate
operations can be processed in a single pass, whether sequential or parallel,
with minimal data buffering.

Further, some operations are deemed short-circuiting operations.
An intermediate operation is short-circuiting if, when presented with
infinite input, it may produce a finite stream as a result. A terminal
operation is short-circuiting if, when presented with infinite input, it may
terminate in finite time. Having a short-circuiting operation in the pipeline
is a necessary, but not sufficient, condition for the processing of an infinite
stream to terminate normally in finite time.

Parallelism

Processing elements with an explicit for-loop is inherently serial.
Streams facilitate parallel execution by reframing the computation as a pipeline of
aggregate operations, rather than as imperative operations on each individual
element. All streams operations can execute either in serial or in parallel.
The stream implementations in the JDK create serial streams unless parallelism is
explicitly requested. For example, Collection has methods
Collection.stream() and Collection.parallelStream(),
which produce sequential and parallel streams respectively; other
stream-bearing methods such as IntStream.range(int, int)
produce sequential streams but these streams can be efficiently parallelized by
invoking their BaseStream.parallel() method.
To execute the prior "sum of weights of widgets" query in parallel, we would
do:

The only difference between the serial and parallel versions of this
example is the creation of the initial stream, using "parallelStream()"
instead of "stream()". When the terminal operation is initiated,
the stream pipeline is executed sequentially or in parallel depending on the
orientation of the stream on which it is invoked. Whether a stream will execute in serial or
parallel can be determined with the isParallel() method, and the
orientation of a stream can be modified with the
BaseStream.sequential() and
BaseStream.parallel() operations. When the terminal
operation is initiated, the stream pipeline is executed sequentially or in
parallel depending on the mode of the stream on which it is invoked.

Except for operations identified as explicitly nondeterministic, such
as findAny(), whether a stream executes sequentially or in parallel
should not change the result of the computation.

Most stream operations accept parameters that describe user-specified
behavior, which are often lambda expressions. To preserve correct behavior,
these behavioral parameters must be non-interfering, and in
most cases must be stateless. Such parameters are always instances
of a functional interface such
as Function, and are often lambda expressions or
method references.

Streams enable you to execute possibly-parallel aggregate operations over a
variety of data sources, including even non-thread-safe collections such as
ArrayList. This is possible only if we can prevent
interference with the data source during the execution of a stream
pipeline. Except for the escape-hatch operations iterator() and
spliterator(), execution begins when the terminal operation is
invoked, and ends when the terminal operation completes. For most data
sources, preventing interference means ensuring that the data source is
not modified at all during the execution of the stream pipeline.
The notable exception to this are streams whose sources are concurrent
collections, which are specifically designed to handle concurrent modification.
Concurrent stream sources are those whose Spliterator reports the
CONCURRENT characteristic.

Accordingly, behavioral parameters in stream pipelines whose source might
not be concurrent should never modify the stream's data source.
A behavioral parameter is said to interfere with a non-concurrent
data source if it modifies, or causes to be
modified, the stream's data source. The need for non-interference applies
to all pipelines, not just parallel ones. Unless the stream source is
concurrent, modifying a stream's data source during execution of a stream
pipeline can cause exceptions, incorrect answers, or nonconformant behavior.
For well-behaved stream sources, the source can be modified before the
terminal operation commences and those modifications will be reflected in
the covered elements. For example, consider the following code:

First a list is created consisting of two strings: "one"; and "two". Then a
stream is created from that list. Next the list is modified by adding a third
string: "three". Finally the elements of the stream are collected and joined
together. Since the list was modified before the terminal collect
operation commenced the result will be a string of "one two three". All the
streams returned from JDK collections, and most other JDK classes,
are well-behaved in this manner; for streams generated by other libraries, see
Low-level stream
construction for requirements for building well-behaved streams.

Stream pipeline results may be nondeterministic or incorrect if the behavioral
parameters to the stream operations are stateful. A stateful lambda
(or other object implementing the appropriate functional interface) is one
whose result depends on any state which might change during the execution
of the stream pipeline. An example of a stateful lambda is the parameter
to map() in:

Here, if the mapping operation is performed in parallel, the results for the
same input could vary from run to run, due to thread scheduling differences,
whereas, with a stateless lambda expression the results would always be the
same.

Note also that attempting to access mutable state from behavioral parameters
presents you with a bad choice with respect to safety and performance; if
you do not synchronize access to that state, you have a data race and
therefore your code is broken, but if you do synchronize access to that
state, you risk having contention undermine the parallelism you are seeking
to benefit from. The best approach is to avoid stateful behavioral
parameters to stream operations entirely; there is usually a way to
restructure the stream pipeline to avoid statefulness.

Side-effects

Side-effects in behavioral parameters to stream operations are, in general,
discouraged, as they can often lead to unwitting violations of the
statelessness requirement, as well as other thread-safety hazards.

If the behavioral parameters do have side-effects, unless explicitly
stated, there are no guarantees as to the
visibility
of those side-effects to other threads, nor are there any guarantees that
different operations on the "same" element within the same stream pipeline
are executed in the same thread. Further, the ordering of those effects
may be surprising. Even when a pipeline is constrained to produce a
result that is consistent with the encounter order of the stream
source (for example, IntStream.range(0,5).parallel().map(x -> x*2).toArray()
must produce [0, 2, 4, 6, 8]), no guarantees are made as to the order
in which the mapper function is applied to individual elements, or in what
thread any behavioral parameter is executed for a given element.

Many computations where one might be tempted to use side effects can be more
safely and efficiently expressed without side-effects, such as using
reduction instead of mutable
accumulators. However, side-effects such as using println() for debugging
purposes are usually harmless. A small number of stream operations, such as
forEach() and peek(), can operate only via side-effects;
these should be used with care.

As an example of how to transform a stream pipeline that inappropriately
uses side-effects to one that does not, the following code searches a stream
of strings for those matching a given regular expression, and puts the
matches in a list.

This code unnecessarily uses side-effects. If executed in parallel, the
non-thread-safety of ArrayList would cause incorrect results, and
adding needed synchronization would cause contention, undermining the
benefit of parallelism. Furthermore, using side-effects here is completely
unnecessary; the forEach() can simply be replaced with a reduction
operation that is safer, more efficient, and more amenable to
parallelization:

Streams may or may not have a defined encounter order. Whether
or not a stream has an encounter order depends on the source and the
intermediate operations. Certain stream sources (such as List or
arrays) are intrinsically ordered, whereas others (such as HashSet)
are not. Some intermediate operations, such as sorted(), may impose
an encounter order on an otherwise unordered stream, and others may render an
ordered stream unordered, such as BaseStream.unordered().
Further, some terminal operations may ignore encounter order, such as
forEach().

If a stream is ordered, most operations are constrained to operate on the
elements in their encounter order; if the source of a stream is a List
containing [1, 2, 3], then the result of executing map(x -> x*2)
must be [2, 4, 6]. However, if the source has no defined encounter
order, then any permutation of the values [2, 4, 6] would be a valid
result.

For sequential streams, the presence or absence of an encounter order does
not affect performance, only determinism. If a stream is ordered, repeated
execution of identical stream pipelines on an identical source will produce
an identical result; if it is not ordered, repeated execution might produce
different results.

For parallel streams, relaxing the ordering constraint can sometimes enable
more efficient execution. Certain aggregate operations,
such as filtering duplicates (distinct()) or grouped reductions
(Collectors.groupingBy()) can be implemented more efficiently if ordering of elements
is not relevant. Similarly, operations that are intrinsically tied to encounter order,
such as limit(), may require
buffering to ensure proper ordering, undermining the benefit of parallelism.
In cases where the stream has an encounter order, but the user does not
particularly care about that encounter order, explicitly de-ordering
the stream with unordered() may
improve parallel performance for some stateful or terminal operations.
However, most stream pipelines, such as the "sum of weight of blocks" example
above, still parallelize efficiently even under ordering constraints.

A reduction operation (also called a fold) takes a sequence
of input elements and combines them into a single summary result by repeated
application of a combining operation, such as finding the sum or maximum of
a set of numbers, or accumulating elements into a list. The streams classes have
multiple forms of general reduction operations, called
reduce()
and collect(),
as well as multiple specialized reduction forms such as
sum(), max(),
or count().

Of course, such operations can be readily implemented as simple sequential
loops, as in:

int sum = 0;
for (int x : numbers) {
sum += x;
}

However, there are good reasons to prefer a reduce operation
over a mutative accumulation such as the above. Not only is a reduction
"more abstract" -- it operates on the stream as a whole rather than individual
elements -- but a properly constructed reduce operation is inherently
parallelizable, so long as the function(s) used to process the elements
are associative and
stateless.
For example, given a stream of numbers for which we want to find the sum, we
can write:

int sum = numbers.stream().reduce(0, (x,y) -> x+y);

or:

int sum = numbers.stream().reduce(0, Integer::sum);

These reduction operations can run safely in parallel with almost no
modification:

int sum = numbers.parallelStream().reduce(0, Integer::sum);

Reduction parallellizes well because the implementation
can operate on subsets of the data in parallel, and then combine the
intermediate results to get the final correct answer. (Even if the language
had a "parallel for-each" construct, the mutative accumulation approach would
still required the developer to provide
thread-safe updates to the shared accumulating variable sum, and
the required synchronization would then likely eliminate any performance gain from
parallelism.) Using reduce() instead removes all of the
burden of parallelizing the reduction operation, and the library can provide
an efficient parallel implementation with no additional synchronization
required.

The "widgets" examples shown earlier shows how reduction combines with
other operations to replace for loops with bulk operations. If widgets
is a collection of Widget objects, which have a getWeight method,
we can find the heaviest widget with:

Here, the identity element is both an initial seed value for the reduction
and a default result if there are no input elements. The accumulator
function takes a partial result and the next element, and produces a new
partial result. The combiner function combines two partial results
to produce a new partial result. (The combiner is necessary in parallel
reductions, where the input is partitioned, a partial accumulation computed
for each partition, and then the partial results are combined to produce a
final result.)

More formally, the identity value must be an identity for
the combiner function. This means that for all u,
combiner.apply(identity, u) is equal to u. Additionally, the
combiner function must be associative and
must be compatible with the accumulator function: for all u
and t, combiner.apply(u, accumulator.apply(identity, t)) must
be equals() to accumulator.apply(u, t).

The three-argument form is a generalization of the two-argument form,
incorporating a mapping step into the accumulation step. We could
re-cast the simple sum-of-weights example using the more general form as
follows:

though the explicit map-reduce form is more readable and therefore should
usually be preferred. The generalized form is provided for cases where
significant work can be optimized away by combining mapping and reducing
into a single function.

A mutable reduction operation accumulates input elements into a
mutable result container, such as a Collection or StringBuilder,
as it processes the elements in the stream.

If we wanted to take a stream of strings and concatenate them into a
single long string, we could achieve this with ordinary reduction:

String concatenated = strings.reduce("", String::concat)

We would get the desired result, and it would even work in parallel. However,
we might not be happy about the performance! Such an implementation would do
a great deal of string copying, and the run time would be O(n^2) in
the number of characters. A more performant approach would be to accumulate
the results into a StringBuilder, which is a mutable
container for accumulating strings. We can use the same technique to
parallelize mutable reduction as we do with ordinary reduction.

The mutable reduction operation is called
collect(),
as it collects together the desired results into a result container such
as a Collection.
A collect operation requires three functions:
a supplier function to construct new instances of the result container, an
accumulator function to incorporate an input element into a result
container, and a combining function to merge the contents of one result
container into another. The form of this is very similar to the general
form of ordinary reduction:

As with reduce(), a benefit of expressing collect in this
abstract way is that it is directly amenable to parallelization: we can
accumulate partial results in parallel and then combine them, so long as the
accumulation and combining functions satisfy the appropriate requirements.
For example, to collect the String representations of the elements in a
stream into an ArrayList, we could write the obvious sequential
for-each form:

Here, our supplier is just the ArrayList constructor, the accumulator adds the stringified element to an
ArrayList, and the combiner simply uses addAll
to copy the strings from one container into the other.

The three aspects of collect -- supplier, accumulator, and
combiner -- are tightly coupled. We can use the abstraction of a
Collector to capture all three aspects. The
above example for collecting strings into a List can be rewritten
using a standard Collector as:

Packaging mutable reductions into a Collector has another advantage:
composability. The class Collectors contains a
number of predefined factories for collectors, including combinators
that transform one collector into another. For example, suppose we have a
collector that computes the sum of the salaries of a stream of
employees, as follows:

(The ? for the second type parameter merely indicates that we don't
care about the intermediate representation used by this collector.)
If we wanted to create a collector to tabulate the sum of salaries by
department, we could reuse summingSalaries using
groupingBy:

As with the regular reduction operation, collect() operations can
only be parallelized if appropriate conditions are met. For any partially
accumulated result, combining it with an empty result container must
produce an equivalent result. That is, for a partially accumulated result
p that is the result of any series of accumulator and combiner
invocations, p must be equivalent to
combiner.apply(p, supplier.get()).

Further, however the computation is split, it must produce an equivalent
result. For any input elements t1 and t2, the results
r1 and r2 in the computation below must be equivalent:

it may actually be counterproductive to perform the operation in parallel.
This is because the combining step (merging one Map into another by
key) can be expensive for some Map implementations.

Suppose, however, that the result container used in this reduction
was a concurrently modifiable collection -- such as a
ConcurrentHashMap. In that case, the parallel
invocations of the accumulator could actually deposit their results
concurrently into the same shared result container, eliminating the need for
the combiner to merge distinct result containers. This potentially provides
a boost to the parallel execution performance. We call this a
concurrent reduction.

A Collector that supports concurrent reduction is
marked with the Collector.Characteristics.CONCURRENT
characteristic. However, a concurrent collection also has a downside. If
multiple threads are depositing results concurrently into a shared container,
the order in which results are deposited is non-deterministic. Consequently,
a concurrent reduction is only possible if ordering is not important for the
stream being processed. The Stream.collect(Collector)
implementation will only perform a concurrent reduction if

Note that if it is important that the elements for a given key appear in
the order they appear in the source, then we cannot use a concurrent
reduction, as ordering is one of the casualties of concurrent insertion.
We would then be constrained to implement either a sequential reduction or
a merge-based parallel reduction.

The class StreamSupport has a number of
low-level methods for creating a stream, all using some form of a
Spliterator. A spliterator is the parallel analogue of an
Iterator; it describes a (possibly infinite) collection of
elements, with support for sequentially advancing, bulk traversal, and
splitting off some portion of the input into another spliterator which can
be processed in parallel. At the lowest level, all streams are driven by a
spliterator.

There are a number of implementation choices in implementing a
spliterator, nearly all of which are tradeoffs between simplicity of
implementation and runtime performance of streams using that spliterator.
The simplest, but least performant, way to create a spliterator is to
create one from an iterator using
Spliterators.spliteratorUnknownSize(java.util.Iterator, int).
While such a spliterator will work, it will likely offer poor parallel
performance, since we have lost sizing information (how big is the
underlying data set), as well as being constrained to a simplistic
splitting algorithm.

A higher-quality spliterator will provide balanced and known-size
splits, accurate sizing information, and a number of other
characteristics of the
spliterator or data that can be used by implementations to optimize
execution.

Spliterators for mutable data sources have an additional challenge;
timing of binding to the data, since the data could change between the time
the spliterator is created and the time the stream pipeline is executed.
Ideally, a spliterator for a stream would report a characteristic of
IMMUTABLE or CONCURRENT; if not it should be
late-binding. If a source
cannot directly supply a recommended spliterator, it may indirectly supply
a spliterator using a Supplier, and construct a stream via the
Supplier-accepting versions of
stream().
The spliterator is obtained from the supplier only after the terminal
operation of the stream pipeline commences.

These requirements significantly reduce the scope of potential
interference between mutations of the stream source and execution of stream
pipelines. Streams based on spliterators with the desired characteristics,
or those using the Supplier-based factory forms, are immune to
modifications of the data source prior to commencement of the terminal
operation (provided the behavioral parameters to the stream operations meet
the required criteria for non-interference and statelessness). See
Non-Interference
for more details.